Workers with the surnames Butcher, Baker, Carpenter and Plumber are currently attending an annual convention.
No-one is currently, nor ever has been in the same profession as their name and no-one has had the same profession twice.
Alan is now a butcher, whereas Mr Brian Butcher used to be a baker. The person who is now a carpenter used to be a butcher. Charles has never been a baker, Mr Darren Carpenter has never been a butcher and Mr Baker is not now a carpenter.
Can you determine their full names, along with their current and previous professions?
Hint
What must the middle midday temperature be? Remember that the temperatures are in degrees Celsius.
Answer
The midday temperatures were -6, -2, 2, 6, 10 °C.
Each day the midday temperature increased by a steady 4 degrees.
Reasoning
As the temperature rose steadily each day, we know that the middle temperature (Day 3) was 2 degrees (because the average was 2 degrees).
Since Day 3 was 2 degrees, and there were two negative temperatures, we know that the daily increase must have been at least 3 degrees (otherwise Day 2 would not have been negative).
If we check a daily increase of 3 degrees, the sequence would be -4, -1, 2, 5, 8, but this doesn't work as the product is less than 500.
If we check a daily increase of 4 degrees, the sequence would be -6, -2, 2, 6, 10, which does match all of the requirements.
If we check a daily increase of 5 degrees, the sequence would be -8, -3, 2, 7, 12, but this doesn't work as the product is more than 2000.
Any larger increase makes the product even larger, so we can stop checking.
